Machine Learning Algorithms Documentation
Geiser, Gruen, Hefti, Kuster
08/01/2021
#Data preparation
Dataset - German Housing Data
Origin data set cleaned:
Variable rooms, bathrooms, bedrooms, floors, garages, Year_built, Year_renovated changed from decimal to integer Subset with buildings up to 20 rooms for our analysis created Rooms with .5 rounded up Levels of the variable Energy_source and Garagetype transformed.
Load of the cleaned dataset
data <- read.csv('german_housing_cleaned.csv',header =T, encoding='UTF-8')
head(data)## Price Type Living_space Lot Rooms Bedrooms Bathrooms Floors
## 1 498000 Multiple dwelling 106.00 229 5 3 1 2
## 2 495000 Mid-terrace house 140.93 517 6 3 2 NA
## 3 749000 Farmhouse 162.89 82 5 3 2 4
## 4 259000 Farmhouse 140.00 814 4 NA 2 2
## 5 469000 Multiple dwelling 115.00 244 4 2 1 NA
## 6 1400000 Mid-terrace house 310.00 860 8 NA NA 3
## Year_built Furnishing_quality Year_renovated Condition Heating
## 1 2005 normal NA refurbished central heating
## 2 1994 basic NA refurbished stove heating
## 3 2013 NA dilapidated stove heating
## 4 1900 basic 2000 fixer-upper central heating
## 5 1968 refined 2019 refurbished central heating
## 6 1969 basic NA maintained
## Energy_source Energy_efficiency_class State City
## 1 natural gas D Baden-Württemberg Bodenseekreis
## 2 Baden-Württemberg Konstanz (Kreis)
## 3 district heating B Baden-Württemberg Esslingen (Kreis)
## 4 electricity G Baden-Württemberg Waldshut (Kreis)
## 5 oil F Baden-Württemberg Esslingen (Kreis)
## 6 oil Baden-Württemberg Stuttgart
## Place Garages Garagetype
## 1 Bermatingen 2 Parking lot
## 2 Engen 7 Parking lot
## 3 Ostfildern 1 Garage
## 4 Bonndorf im Schwarzwald 1 Garage
## 5 Leinfelden-Echterdingen 1 Garage
## 6 Süd 2 GarageInspection of all variables
str(data)
summary(data)
colnames(data)
apply(data,2,function(x) sum(is.na(x)))Analysis of the distribution of the variables: ‘Price’, ‘Living_space’, ‘Rooms’ and ‘Lot’
par(mfrow = c(2,2))
#Price
plot(density(data$Price))
#Living_space
plot(density(data$Living_space))
#Rooms
hist(data$Rooms)
#Lot
plot(density(data$Lot))
Result: The variables are right skewed
Log Transformation of variables
Therefore we will use the Log Transformation of the variables ‘Price’, ‘Living_space’, ‘Rooms’, ‘Lot’ to get a nearly normal distribution
par(mfrow = c(2,2))
#Price
price.log <- density(log(data$Price))
plot(price.log)
#Living_space
living.log <- density(log(data$Living_space))
plot(living.log)
#Rooms
rooms.log <- log(data$Rooms)
hist(rooms.log)
#Lot
lot.log <- density(log(data$Lot))
plot(lot.log)
Add new columns with log transformed variables price, living space and rooms
data1 <- data
data1$log.price <- log(data1$Price)
data1$log.living <- log(data1$Living_space)
data1$log.rooms <- log(data1$Rooms)
data1$log.lot <- log(data1$Lot)
data1$Condition <- factor(data1$Condition)
#str(data1)1 Week 1 - Linear Models
1.1 Data Visualisation and Linear regressions
The variables Price, Living_space and Rooms are checked for na values
options(scipen=999) #block scientific notation
library(ggplot2)
attach(data)1.2 Scatterplot with regression line for log(Price) against log(Living_space)
We plot the response variable “Price” against the predictor “Living_Space” to get a first impression and grahical analysis.
#Living_space
ggplot(data1, aes(log.living, log.price)) + geom_point() + geom_smooth(method = lm, se = T, color = 'red') + ggtitle('Scatterplot with regression line for log(Price) against log.living')
1.3 Fitting a Simple Linear regression of log(Price) against log(Living_space) and check the coefficients
#linear model
lm.log.price_living <- lm(log.price ~ log.living, data = data1)
summary(lm.log.price_living)##
## Call:
## lm(formula = log.price ~ log.living, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.7836 -0.4079 0.0856 0.4683 2.7581
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.17522 0.07596 107.62 <0.0000000000000002 ***
## log.living 0.90280 0.01455 62.05 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7145 on 10316 degrees of freedom
## Multiple R-squared: 0.2718, Adjusted R-squared: 0.2717
## F-statistic: 3850 on 1 and 10316 DF, p-value: < 0.00000000000000022#estimated regression coefficients
coef(lm.log.price_living)## (Intercept) log.living
## 8.1752232 0.9028032exp(coef(lm.log.price_living))## (Intercept) log.living
## 3551.847713 2.466508#p-values
summary(lm.log.price_living)$coefficients## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.1752232 0.07596044 107.62475 0
## log.living 0.9028032 0.01455063 62.04563 0Result: very significant p-values for Price ~ Living_space. We can assume that the variable Living_space has an effect on the dependent variable (Price) with a positive correlation, meaning: if the Living_space parameter increase in value also the Price of the property will increase.
We interpret the intercept and the second coefficient, the slope, we exponentiate the values. The results are: For the intercept exp(8.17522)= 3551.84 and the slope exp(0.9028)=2.47
Interpretation: It seems to be a positive relationship between these two variables. More livingspace seems to have a higher price. So we fit a simple regression model to the data. With a livingspace of 0 the price would be 3551.84 EURO and with each unit increase of the livingspace the price increase by 2.47 EURO which does not make much sense. The p-value is very small therefore we have a strong evidence that the slope for livingspace is not flat.
1.4 Linear regression of log(Price) against log(Living_space) including the Type and finding the intercept for the different Types.
##linear model
lm.log.price_living_type <- lm(data = data1, log.price ~ log.living + Type)
summary(lm.log.price_living_type)##
## Call:
## lm(formula = log.price ~ log.living + Type, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9802 -0.3849 0.0716 0.4556 2.7356
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.47225 0.09409 79.414 < 0.0000000000000002 ***
## log.living 0.99691 0.01679 59.378 < 0.0000000000000002 ***
## TypeBungalow 0.24691 0.05737 4.304 0.000016956457415 ***
## TypeCastle -0.33356 0.31169 -1.070 0.284573
## TypeCorner house -0.14759 0.06058 -2.436 0.014857 *
## TypeDuplex -0.06320 0.03900 -1.620 0.105186
## TypeFarmhouse 0.26026 0.04599 5.659 0.000000015603919 ***
## TypeMid-terrace house 0.24470 0.03679 6.651 0.000000000030494 ***
## TypeMultiple dwelling 0.35983 0.05029 7.155 0.000000000000891 ***
## TypeResidential property 0.17411 0.05094 3.418 0.000634 ***
## TypeSingle dwelling 0.39721 0.04091 9.708 < 0.0000000000000002 ***
## TypeSpecial property 0.46909 0.05103 9.193 < 0.0000000000000002 ***
## TypeVilla 0.70309 0.05077 13.847 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6912 on 10305 degrees of freedom
## Multiple R-squared: 0.3193, Adjusted R-squared: 0.3185
## F-statistic: 402.8 on 12 and 10305 DF, p-value: < 0.00000000000000022#estimated regression coefficients
coef(lm.log.price_living_type)## (Intercept) log.living TypeBungalow
## 7.4722543 0.9969080 0.2469139
## TypeCastle TypeCorner house TypeDuplex
## -0.3335592 -0.1475928 -0.0631954
## TypeFarmhouse TypeMid-terrace house TypeMultiple dwelling
## 0.2602565 0.2447012 0.3598267
## TypeResidential property TypeSingle dwelling TypeSpecial property
## 0.1741124 0.3972086 0.4690858
## TypeVilla
## 0.7030881#intercept of Type "NULL"
coef(lm.log.price_living_type)['(Intercept)']## (Intercept)
## 7.472254#intercept of Type single dwelling
coef(lm.log.price_living_type)['(Intercept)'] + coef(lm.log.price_living_type)['TypeSingle dwelling']## (Intercept)
## 7.8694631.5 Linear regression of log(Price) against log(Living_space) including the Type interaction
##linear model
lm.log.price_living_type2 <- lm(data = data1, log.price ~ log.living * Type)
summary(lm.log.price_living_type2)##
## Call:
## lm(formula = log.price ~ log.living * Type, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.0574 -0.3835 0.0672 0.4576 2.7139
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 7.73609 0.27923 27.705
## log.living 0.94614 0.05331 17.749
## TypeBungalow 0.92173 0.48628 1.895
## TypeCastle -1.04467 5.02138 -0.208
## TypeCorner house -0.80053 0.58144 -1.377
## TypeDuplex 1.34421 0.35134 3.826
## TypeFarmhouse 0.63145 0.53470 1.181
## TypeMid-terrace house -0.68139 0.31354 -2.173
## TypeMultiple dwelling 0.24793 0.69059 0.359
## TypeResidential property -0.31372 0.45320 -0.692
## TypeSingle dwelling -0.75763 0.42213 -1.795
## TypeSpecial property -0.77518 0.45681 -1.697
## TypeVilla 0.06219 0.60861 0.102
## log.living:TypeBungalow -0.11718 0.08861 -1.322
## log.living:TypeCastle 0.12151 0.79328 0.153
## log.living:TypeCorner house 0.12396 0.10936 1.133
## log.living:TypeDuplex -0.24967 0.06560 -3.806
## log.living:TypeFarmhouse -0.08080 0.10831 -0.746
## log.living:TypeMid-terrace house 0.18009 0.06011 2.996
## log.living:TypeMultiple dwelling 0.01967 0.13964 0.141
## log.living:TypeResidential property 0.09284 0.08538 1.087
## log.living:TypeSingle dwelling 0.23218 0.08354 2.779
## log.living:TypeSpecial property 0.25164 0.09095 2.767
## log.living:TypeVilla 0.11600 0.10750 1.079
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## log.living < 0.0000000000000002 ***
## TypeBungalow 0.058061 .
## TypeCastle 0.835198
## TypeCorner house 0.168607
## TypeDuplex 0.000131 ***
## TypeFarmhouse 0.237658
## TypeMid-terrace house 0.029787 *
## TypeMultiple dwelling 0.719593
## TypeResidential property 0.488813
## TypeSingle dwelling 0.072720 .
## TypeSpecial property 0.089737 .
## TypeVilla 0.918609
## log.living:TypeBungalow 0.186066
## log.living:TypeCastle 0.878261
## log.living:TypeCorner house 0.257038
## log.living:TypeDuplex 0.000142 ***
## log.living:TypeFarmhouse 0.455705
## log.living:TypeMid-terrace house 0.002741 **
## log.living:TypeMultiple dwelling 0.887975
## log.living:TypeResidential property 0.276883
## log.living:TypeSingle dwelling 0.005460 **
## log.living:TypeSpecial property 0.005673 **
## log.living:TypeVilla 0.280593
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6879 on 10294 degrees of freedom
## Multiple R-squared: 0.3264, Adjusted R-squared: 0.3249
## F-statistic: 216.9 on 23 and 10294 DF, p-value: < 0.00000000000000022#estimated regression coefficients
coef(lm.log.price_living_type2)## (Intercept) log.living
## 7.73608549 0.94613962
## TypeBungalow TypeCastle
## 0.92172518 -1.04467031
## TypeCorner house TypeDuplex
## -0.80052753 1.34420839
## TypeFarmhouse TypeMid-terrace house
## 0.63144756 -0.68139164
## TypeMultiple dwelling TypeResidential property
## 0.24793247 -0.31371529
## TypeSingle dwelling TypeSpecial property
## -0.75763067 -0.77518375
## TypeVilla log.living:TypeBungalow
## 0.06219264 -0.11718366
## log.living:TypeCastle log.living:TypeCorner house
## 0.12151270 0.12396267
## log.living:TypeDuplex log.living:TypeFarmhouse
## -0.24967456 -0.08079852
## log.living:TypeMid-terrace house log.living:TypeMultiple dwelling
## 0.18008764 0.01967192
## log.living:TypeResidential property log.living:TypeSingle dwelling
## 0.09283769 0.23217929
## log.living:TypeSpecial property log.living:TypeVilla
## 0.25164379 0.11599769# The "P-Values - confidence intervals" duality
confint(lm.log.price_living_type2)## 2.5 % 97.5 %
## (Intercept) 7.18873463 8.28343635
## log.living 0.84164786 1.05063138
## TypeBungalow -0.03148560 1.87493595
## TypeCastle -10.88754235 8.79820173
## TypeCorner house -1.94027217 0.33921710
## TypeDuplex 0.65550987 2.03290692
## TypeFarmhouse -0.41667545 1.67957057
## TypeMid-terrace house -1.29599299 -0.06679028
## TypeMultiple dwelling -1.10576712 1.60163207
## TypeResidential property -1.20207438 0.57464379
## TypeSingle dwelling -1.58509414 0.06983281
## TypeSpecial property -1.67062159 0.12025410
## TypeVilla -1.13079934 1.25518461
## log.living:TypeBungalow -0.29088557 0.05651824
## log.living:TypeCastle -1.43346849 1.67649390
## log.living:TypeCorner house -0.09041307 0.33833842
## log.living:TypeDuplex -0.37826357 -0.12108555
## log.living:TypeFarmhouse -0.29311479 0.13151774
## log.living:TypeMid-terrace house 0.06226578 0.29790949
## log.living:TypeMultiple dwelling -0.25405926 0.29340310
## log.living:TypeResidential property -0.07451478 0.26019016
## log.living:TypeSingle dwelling 0.06841797 0.39594061
## log.living:TypeSpecial property 0.07335498 0.42993261
## log.living:TypeVilla -0.09472399 0.32671936Result: mostly very significant p-values for Price ~ Living_space and different types. Only TypeCastle and TypeDuplex with non significant values. We can assume that the different types have different impact on the variable Price against Living_space.
Interpretation of the coefficients of Type variable: Intercept for TypeSingle Dwelling: exp(7.869463) with Slope: exp(0.9969080)
1.5.1 Measures of fit
formula(lm.log.price_living_type)## log.price ~ log.living + Type#r.squared
summary(lm.log.price_living_type)$r.squared## [1] 0.3192727#adj.r.squared
summary(lm.log.price_living_type)$adj.r.squared## [1] 0.31848formula(lm.log.price_living_type2)## log.price ~ log.living * Type#r.squared
summary(lm.log.price_living_type2)$r.squared## [1] 0.3263949#adj.r.squared
summary(lm.log.price_living_type2)$adj.r.squared## [1] 0.32488991.6 Linear regression of log(Price) against log(Rooms)
In an next step we examine the data set graphically and consider again “Price” as response variable but as predictor “Rooms” and we fit the model again with a simple linear regression.
1.6.1 Measures of fit
formula(lm.log.price_rooms)## log(Price) ~ log(Rooms)#r.squared
summary(lm.log.price_rooms)$r.squared## [1] 0.09968285#adj.r.squared
summary(lm.log.price_rooms)$adj.r.squared## [1] 0.099595581.7 Linear regression of log(Price) against Type
Now we are modelling a linear regression with dependent variable ‘Price’ and the categorical variable “Type” as independent variable. First we visualize the variable ‘Type’ with a boxplot with and one without outliers.
1.8 Fitted values
The function fitted() can be used to extract the predicted values for the existing observations
attach(data)## The following objects are masked from data (pos = 3):
##
## Bathrooms, Bedrooms, City, Condition, Energy_efficiency_class,
## Energy_source, Floors, Furnishing_quality, Garages, Garagetype,
## Heating, Living_space, Lot, Place, Price, Rooms, State, Type,
## Year_built, Year_renovated#lm.log.price_living
fitted.price_living <- fitted(lm.log.price_living)
str(fitted.price_living)## Named num [1:10318] 12.4 12.6 12.8 12.6 12.5 ...
## - attr(*, "names")= chr [1:10318] "1" "2" "3" "4" ...head(fitted.price_living)## 1 2 3 4 5 6
## 12.38539 12.64253 12.77327 12.63655 12.45896 13.35422plot(log(Price)~ log(Living_space), main = 'Model log(Price) ~ log(Living_space)', col = 'navy', pch = 16)
points(fitted.price_living ~ log(Living_space), col = 'red', pch = 16)
abline(lm.log.price_living, col = 'yellow', lwd = 2.5)
1.9 Residuals of model log(Price) ~ log(Living_space)
attach(data1)
resid.price_living <- resid(lm.log.price_living)
length(resid.price_living)## [1] 10318head(resid.price_living)## 1 2 3 4 5 6
## 0.7329643 0.4697818 0.7532264 -0.1719706 0.5993948 0.7977636set.seed(100)
id <- sample(x = 1:10318, size = 5)
resid.price_living[id]## 3786 503 3430 3696 4090
## 0.5106768 -0.3315001 0.4470366 -0.9261093 1.0834033fitted.price_living[id]## 3786 503 3430 3696 4090
## 13.77484 12.69884 13.46378 12.41883 13.03221plot(log(Price) ~ log(Living_space), main = 'Model log(Price) ~ log(Living_space)', col = 'navy', pch = 16)
abline(lm.log.price_living, col = 'green', lwd = 2.5)
points(log(Price) ~ log(Living_space), data = data1[id, ], col = 'red', pch = 4, lwd = 5)
segments(x0 = data1[id, 'log.living'], x1 = data1[id, 'log.living'],
y0 = fitted.price_living[id], y1 = data1[id, 'log.price'], col = 'yellow', lwd = 2)
1.10 Predicting values using splitted data set 80:20 ratio
#split dataset
split80 <- round(nrow(data1)* 0.80)
train <- data1[1:split80,]
test <- data1[(split80 + 1):nrow(data1),]
dim(train)## [1] 8254 24dim(test)## [1] 2064 24#linear regression model
lm.train <- lm(log.price ~ log.living, data = train)
summary(lm.train)##
## Call:
## lm(formula = log.price ~ log.living, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.8765 -0.3774 0.0557 0.4283 2.6734
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.45284 0.07981 105.91 <0.0000000000000002 ***
## log.living 0.86819 0.01524 56.96 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6563 on 8252 degrees of freedom
## Multiple R-squared: 0.2822, Adjusted R-squared: 0.2821
## F-statistic: 3245 on 1 and 8252 DF, p-value: < 0.00000000000000022#predictions
pred.new.living <- predict(object = lm.train, newdata = test)
pred.new.living.CI <- predict(object = lm.train, interval = 'prediction', newdata = test)
#display predictions
plot(log.price ~log.living, data = data1, main = 'Prediction with Model log(Price) ~ log(Living_space)', col = 'navy', pch = 16)
points(x = test$log.living, y= pred.new.living, col = 'red', pch = 16, cex = 1.5)
abline(lm.train, col = 'yellow', lwd = 2.5)
plot(log.price ~ log.living, data = train, main = 'Prediction with Model log(Price) ~ log(Living_space)', col = 'navy', pch = 16)
segments(x0 = test$log.living, x1 = test$log.living,
y0 = pred.new.living.CI[, 'lwr'], y1 = pred.new.living.CI[, 'upr'], lwd = 2, col = 'green')
points(x = test$log.living, y= pred.new.living.CI[,'fit'], col = 'red', pch = 16, cex =1.5)
abline(lm.train, col = 'yellow', lwd = 2.5)
1.11 Testing the effect of a categorical variable and post-hoc contrasts
condition.box.with_outlier <- ggplot(data1, aes(x=Condition, y=log.price)) + geom_boxplot(outlier.colour = 'red')+ theme(axis.text.x = element_text(angle = 90)) + ggtitle('Boxplots of log(Price) against Condition with outliers in red')
plot(condition.box.with_outlier)
#model
lm.price_condition.1 <- lm(log.price ~ Condition, data = data1)
summary(lm.price_condition.1)##
## Call:
## lm(formula = log.price ~ Condition, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6043 -0.4304 0.0333 0.4884 3.6247
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) 12.95695 0.04213 307.553
## Conditionas new -1.01885 0.24696 -4.126
## Conditiondilapidated 0.47108 0.04838 9.738
## Conditionfirst occupation 0.19331 0.09330 2.072
## Conditionfirst occupation after refurbishment -0.05091 0.05685 -0.895
## Conditionfixer-upper -0.10881 0.05398 -2.016
## Conditionmaintained -0.42435 0.04906 -8.649
## Conditionrefurbished -0.14229 0.04328 -3.288
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## Conditionas new 0.0000373 ***
## Conditiondilapidated < 0.0000000000000002 ***
## Conditionfirst occupation 0.03829 *
## Conditionfirst occupation after refurbishment 0.37055
## Conditionfixer-upper 0.04384 *
## Conditionmaintained < 0.0000000000000002 ***
## Conditionrefurbished 0.00101 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8071 on 10310 degrees of freedom
## Multiple R-squared: 0.07146, Adjusted R-squared: 0.07083
## F-statistic: 113.4 on 7 and 10310 DF, p-value: < 0.00000000000000022#coefficients
coef(lm.price_condition.1)## (Intercept)
## 12.95694626
## Conditionas new
## -1.01884973
## Conditiondilapidated
## 0.47108462
## Conditionfirst occupation
## 0.19330741
## Conditionfirst occupation after refurbishment
## -0.05090966
## Conditionfixer-upper
## -0.10881029
## Conditionmaintained
## -0.42434950
## Conditionrefurbished
## -0.14228677aggregate(log.price ~Condition,
FUN = mean, data = data1)## Condition log.price
## 1 12.95695
## 2 as new 11.93810
## 3 dilapidated 13.42803
## 4 first occupation 13.15025
## 5 first occupation after refurbishment 12.90604
## 6 fixer-upper 12.84814
## 7 maintained 12.53260
## 8 refurbished 12.81466#model without slope, only intercept
lm.price_condition.0 <- lm(log.price ~ 1, data = data1)
summary(lm.price_condition.0)##
## Call:
## lm(formula = log.price ~ 1, data = data1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6576 -0.4388 0.0287 0.5166 3.5125
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.867983 0.008243 1561 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8373 on 10317 degrees of freedomcoef(lm.price_condition.0)## (Intercept)
## 12.86798#Anova
anova(lm.price_condition.0, lm.price_condition.1)## Analysis of Variance Table
##
## Model 1: log.price ~ 1
## Model 2: log.price ~ Condition
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 10317 7232.5
## 2 10310 6715.7 7 516.86 113.36 < 0.00000000000000022 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#post-hoc contrasts
library(multcomp)
unique(data1$Condition)## [1] refurbished dilapidated
## [3] fixer-upper maintained
## [5] as new
## [7] first occupation after refurbishment first occupation
## 8 Levels: as new dilapidated ... refurbishedph.test.1 <- glht(model = lm.price_condition.1, linfct = mcp(Condition = c('refurbished - dilapidated = 0')))
summary(ph.test.1)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: User-defined Contrasts
##
##
## Fit: lm(formula = log.price ~ Condition, data = data1)
##
## Linear Hypotheses:
## Estimate Std. Error t value Pr(>|t|)
## refurbished - dilapidated == 0 -0.61337 0.02576 -23.81 <0.0000000000000002
##
## refurbished - dilapidated == 0 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)R uses “treatment contrasts” and therefore the Intercept refers to the first in alphabetical order, here “Null”. The other coefficients represent the difference.
1.12 Adding more categorical variables to the testing above
#str(data1)
Year_built1 <- as.integer(data1$Year_built)
floor1 <- as.integer(data1$Floors)
typeof(Year_built1)## [1] "integer"lm.price_condition.2 <- update(lm.price_condition.1,. ~ . + Type + log.rooms + State +Energy_efficiency_class + Year_built1 + Furnishing_quality + floor1)
formula(lm.price_condition.2)## log.price ~ Condition + Type + log.rooms + State + Energy_efficiency_class +
## Year_built1 + Furnishing_quality + floor1drop1(lm.price_condition.2, test = "F")## Single term deletions
##
## Model:
## log.price ~ Condition + Type + log.rooms + State + Energy_efficiency_class +
## Year_built1 + Furnishing_quality + floor1
## Df Sum of Sq RSS AIC F value
## <none> 2148.4 -8631.8
## Condition 7 17.57 2165.9 -8587.1 8.3684
## Type 11 134.63 2283.0 -8215.5 40.7950
## log.rooms 1 152.62 2301.0 -8138.9 508.7221
## State 15 638.74 2787.1 -6784.8 141.9381
## Energy_efficiency_class 9 33.56 2181.9 -8538.0 12.4294
## Year_built1 1 56.88 2205.2 -8445.4 189.5786
## Furnishing_quality 4 346.08 2494.4 -7562.8 288.3902
## floor1 1 31.86 2180.2 -8527.7 106.1896
## Pr(>F)
## <none>
## Condition 0.0000000003205 ***
## Type < 0.00000000000000022 ***
## log.rooms < 0.00000000000000022 ***
## State < 0.00000000000000022 ***
## Energy_efficiency_class < 0.00000000000000022 ***
## Year_built1 < 0.00000000000000022 ***
## Furnishing_quality < 0.00000000000000022 ***
## floor1 < 0.00000000000000022 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 11.13 Testing categorical variable (Furnishing_quality)and comparing by F-test (Soll das hier noch rein ??)
2 Week 2 - Non-linearity
2.1 Polynomials
By including polynomials (e.g. x1 + x1^2) we can model non linear relationships with a Linear Model.
library(ggplot2)
attach(data1)Graphical analysis
log(Price) ~ log(Living_space)
gg.log.price_log.living <- ggplot(data1,mapping = aes(y = log.price, x = log.living)) + geom_point()
gg.log.price_log.living + geom_smooth()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
gg.log.price_log.living <- ggplot(data1,mapping = aes(y = log.price, x = Year_built1)) + geom_point()
gg.log.price_log.living + geom_smooth()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'## Warning: Removed 666 rows containing non-finite values (stat_smooth).## Warning: Removed 666 rows containing missing values (geom_point).
Quadratic Effects
#model with a linear effect for log.living
lm.living.1 <- lm(log.price ~ log.living + Year_built1)
summary(lm.living.1)##
## Call:
## lm(formula = log.price ~ log.living + Year_built1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6576 -0.3852 0.0262 0.4060 3.9425
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.2750992 0.2533033 -5.034 0.000000489 ***
## log.living 0.9446621 0.0139966 67.492 < 0.0000000000000002 ***
## Year_built1 0.0047208 0.0001203 39.234 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6523 on 9649 degrees of freedom
## (666 observations deleted due to missingness)
## Multiple R-squared: 0.369, Adjusted R-squared: 0.3689
## F-statistic: 2822 on 2 and 9649 DF, p-value: < 0.00000000000000022#model with a quadratic effect for log.living
lm.living.2 <- update(lm.living.1, . ~ . + I(log.living^2))
summary(lm.living.2)##
## Call:
## lm(formula = log.price ~ log.living + Year_built1 + I(log.living^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6813 -0.3840 0.0215 0.4053 4.1527
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.8930634 0.5350769 -7.276 0.000000000000371 ***
## log.living 1.9999960 0.1905934 10.494 < 0.0000000000000002 ***
## Year_built1 0.0046546 0.0001207 38.553 < 0.0000000000000002 ***
## I(log.living^2) -0.1004879 0.0180993 -5.552 0.000000028983449 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6513 on 9648 degrees of freedom
## (666 observations deleted due to missingness)
## Multiple R-squared: 0.3711, Adjusted R-squared: 0.3709
## F-statistic: 1897 on 3 and 9648 DF, p-value: < 0.00000000000000022#test in quadratic
anova(lm.living.1, lm.living.2)## Analysis of Variance Table
##
## Model 1: log.price ~ log.living + Year_built1
## Model 2: log.price ~ log.living + Year_built1 + I(log.living^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 9649 4106.2
## 2 9648 4093.1 1 13.077 30.825 0.00000002898 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#plot
gg.log.price_log.living + geom_smooth(method = 'lm', formula = y ~poly(x, degree = 2))## Warning: Removed 666 rows containing non-finite values (stat_smooth).## Warning: Removed 666 rows containing missing values (geom_point).
#model with a quadratic poly
lm.living.3 <- lm(log.price ~ log.rooms + log.living + poly(log.living, degree = 2))
summary(lm.living.3)##
## Call:
## lm(formula = log.price ~ log.rooms + log.living + poly(log.living,
## degree = 2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9761 -0.3927 0.0714 0.4552 2.6652
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.36089 0.08734 84.28 <0.0000000000000002
## log.rooms -0.44504 0.02490 -17.88 <0.0000000000000002
## log.living 1.21643 0.02262 53.78 <0.0000000000000002
## poly(log.living, degree = 2)1 NA NA NA NA
## poly(log.living, degree = 2)2 -7.82809 0.70453 -11.11 <0.0000000000000002
##
## (Intercept) ***
## log.rooms ***
## log.living ***
## poly(log.living, degree = 2)1
## poly(log.living, degree = 2)2 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7009 on 10314 degrees of freedom
## Multiple R-squared: 0.2994, Adjusted R-squared: 0.2992
## F-statistic: 1469 on 3 and 10314 DF, p-value: < 0.00000000000000022#model with a cubic poly
lm.living.4 <- lm(log.price ~ log.rooms + log.living + poly(log.living, degree = 3))
summary(lm.living.4)##
## Call:
## lm(formula = log.price ~ log.rooms + log.living + poly(log.living,
## degree = 3))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9763 -0.3928 0.0714 0.4553 2.6650
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.36062 0.08761 84.011 <0.0000000000000002
## log.rooms -0.44519 0.02519 -17.676 <0.0000000000000002
## log.living 1.21654 0.02278 53.412 <0.0000000000000002
## poly(log.living, degree = 3)1 NA NA NA NA
## poly(log.living, degree = 3)2 -7.82850 0.70465 -11.110 <0.0000000000000002
## poly(log.living, degree = 3)3 -0.02715 0.70903 -0.038 0.969
##
## (Intercept) ***
## log.rooms ***
## log.living ***
## poly(log.living, degree = 3)1
## poly(log.living, degree = 3)2 ***
## poly(log.living, degree = 3)3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.701 on 10313 degrees of freedom
## Multiple R-squared: 0.2994, Adjusted R-squared: 0.2991
## F-statistic: 1102 on 4 and 10313 DF, p-value: < 0.00000000000000022gg.log.lot.log.price <- ggplot(data = data1, mapping = aes(y = log.lot, x = log.price)) + geom_point()
gg.log.lot.log.price + geom_smooth(method = 'gam')
2.2 Regression Splines
2.3 Generalised Additive Models - GAMs
GAMs for log(Price) ~ log(Rooms)
gam.log.price.log.rooms <- gam(log.price ~ s(log.rooms))
summary(gam.log.price.log.rooms)##
## Family: gaussian
## Link function: identity
##
## Formula:
## log.price ~ s(log.rooms)
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.867983 0.007783 1653 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(log.rooms) 7.888 8.623 145.8 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.108 Deviance explained = 10.9%
## GCV = 0.62562 Scale est. = 0.62509 n = 10318plot(gam.log.price.log.rooms, residuals = TRUE, cex = 2)
GAMs for log(Price) ~ log(Living_space) + s(Log(Rooms)) + s(log(Garages)
gam.log.price.log.living <- gam(log.price ~ log.living + s(log.rooms) + s(log(Garages)))
summary(gam.log.price.log.living)##
## Family: gaussian
## Link function: identity
##
## Formula:
## log.price ~ log.living + s(log.rooms) + s(log(Garages))
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.46447 0.13313 48.56 <0.0000000000000002 ***
## log.living 1.24132 0.02547 48.74 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(log.rooms) 4.964 6.084 67.976 < 0.0000000000000002 ***
## s(log(Garages)) 8.215 8.681 3.852 0.0000713 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.305 Deviance explained = 30.6%
## GCV = 0.42626 Scale est. = 0.4255 n = 8437plot(gam.log.price.log.living, residuals = TRUE, select = 1)
#stroe the residuals in data1
data1$resid.price_living <- resid(lm.log.price_living)
#creat QQ-Plot
qqnorm(resid(lm.log.price_living))
qqline(resid(lm.log.price_living))
Expected value of the errors is “on zero”
ggplot(mapping = aes(y = resid(lm.log.price_living),
x = fitted(lm.log.price_living))) +
geom_abline(intercept = 0, slope = 0) + geom_point() +
geom_smooth()probably non-linear because the smoother is not on zero
Homoscedasticity
ggplot(mapping = aes(y = abs(resid(lm.log.price_living)), x = fitted(lm.log.price_living))) +
geom_abline(intercept = 0, slope = 0) + geom_point() +
geom_smooth()## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
The variance of the residuals seems to be fairly constant
Cooks distance
## 1) compute Cook’s distance
cooks.dist.log.price_living <- cooks.distance(lm.log.price_living)
##
## 2) plot it
ggplot(data = data1,
mapping = aes(y = log.price, x = log.living,
colour = cooks.dist.log.price_living)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE) + facet_wrap(. ~ Type)## `geom_smooth()` using formula 'y ~ x'
plot(lm.log.price_living, which = 5)
Testing the model assumptions
plot(lm.log.price_living_type)
Bootstrap
#mean(data$Price)
##
B <- 10^3
t.mean <- c()
for(i in 1:B){
t.id <- sample(1:10318, replace = TRUE)
t.data.price <- data$Price[t.id]
t.mean[i] <- mean(t.data.price)
}
##
length(t.mean)## [1] 1000hist(t.mean, breaks = 50)
abline(v = mean(data$Price), col = "red")
sorted.means <- sort(t.mean)
quantile(sorted.means, probs = c(0.025, 0.975))## 2.5% 97.5%
## 529609.2 551910.53 Week 3 - Generalised Linear Models
3.1 GLM - Possion Model
Count Data
With the GLM function and the family “possion” we could generalize the Linear model that the right-skewed data Rooms and Type can be followed without log- transformation in the first place.
#str(data)
glm.rooms <- glm(Rooms ~ Type,
family = "poisson",
data = data)
summary(glm.rooms)##
## Call:
## glm(formula = Rooms ~ Type, family = "poisson", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.6463 -0.6320 -0.0781 0.3702 4.4559
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.02917 0.01848 109.821 < 0.0000000000000002 ***
## TypeBungalow 0.17457 0.02838 6.152 0.000000000766 ***
## TypeCastle 0.55104 0.12447 4.427 0.000009550749 ***
## TypeCorner house 0.01343 0.03162 0.425 0.671
## TypeDuplex 0.26787 0.01981 13.522 < 0.0000000000000002 ***
## TypeFarmhouse -0.43417 0.02638 -16.456 < 0.0000000000000002 ***
## TypeMid-terrace house -0.22653 0.01948 -11.626 < 0.0000000000000002 ***
## TypeMultiple dwelling -0.38499 0.02917 -13.197 < 0.0000000000000002 ***
## TypeResidential property 0.04744 0.02637 1.799 0.072 .
## TypeSingle dwelling -0.38432 0.02252 -17.066 < 0.0000000000000002 ***
## TypeSpecial property -0.47841 0.03056 -15.655 < 0.0000000000000002 ***
## TypeVilla 0.14646 0.02522 5.806 0.000000006387 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 13951.1 on 10317 degrees of freedom
## Residual deviance: 9350.9 on 10306 degrees of freedom
## AIC: 47557
##
## Number of Fisher Scoring iterations: 4#exponential function, is needed duelog() function as link function within glm
exp(coef(glm.rooms)) ## (Intercept) TypeBungalow TypeCastle
## 7.6077922 1.1907296 1.7350632
## TypeCorner house TypeDuplex TypeFarmhouse
## 1.0135214 1.3071727 0.6477992
## TypeMid-terrace house TypeMultiple dwelling TypeResidential property
## 0.7972979 0.6804577 1.0485829
## TypeSingle dwelling TypeSpecial property TypeVilla
## 0.6809147 0.6197703 1.1577330Before the Interpretation of the coefficients of a Poisson model the inverse, the exponential, is needed due to use of the link function (log() function). The Interpretation of the coefficients are: A house with no Type information has around 7.6 rooms and e.g. Villa has ca. 15.77% more rooms (ca. 8.8 rooms)
#to double check single house (type) is checked and predicted
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ tibble 3.0.4 ✓ dplyr 1.0.2
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.4.0 ✓ forcats 0.5.0
## ✓ purrr 0.3.4## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::collapse() masks nlme::collapse()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x dplyr::select() masks MASS::select()#which(data$Type == "")
#data[99,]
fitted.room <- fitted(glm.rooms)[99]
fitted.room## 99
## 7.607792specific.room <- data[99,]
specific.room$Type <- "Villa"
#specific.room
pred.specific.room <- predict(glm.rooms,
type = "response",
newdata = specific.room)
pred.specific.room## 99
## 8.807792fitted.room * exp(coef(glm.rooms)["TypeVilla"])## 99
## 8.807792This house with no specific Type, according to the model, is expected to have 7.607 Rooms. If we check the number of rooms after setting the Type to e.g. Villa the model expect 8.807 rooms and this is exactly the same number of rooms we get for the fitted room times the exponential estimated for Villa
data simulation from the glm count data model
#data simulation from the glm model (glm.rooms)
set.seed(99)
sim.data.rooms.Poisson <- simulate(glm.rooms)
##
NROW(sim.data.rooms.Poisson)## [1] 10318head(sim.data.rooms.Poisson)## sim_1
## 1 5
## 2 3
## 3 6
## 4 11
## 5 5
## 6 11tail(sim.data.rooms.Poisson)## sim_1
## 10313 5
## 10314 4
## 10315 6
## 10316 10
## 10317 6
## 10318 4Visualization of the glm count data model
ggplot(mapping = aes(y = sim.data.rooms.Poisson$sim_1,
x = data$Type)) +
geom_boxplot() +
geom_hline(yintercept = 0) +
ylab("simulated no. of rooms\n(assuming Poisson dist)") +
xlab("type") + theme(axis.text.x = element_text(angle = 90))
The results of the simulation seem to agree with the observation, see for example Type = Villa, but there are some difference due to outliers
GLM with binomial data continious variable
df.glm <- data.frame(data$Price, data$Living_space, data$Year_built)
df.glm <-na.omit(df.glm)
any(is.na(df.glm))## [1] FALSEstr(df.glm)## 'data.frame': 9652 obs. of 3 variables:
## $ data.Price : num 498000 495000 749000 259000 469000 1400000 3500000 630000 364000 1750000 ...
## $ data.Living_space: num 106 141 163 140 115 ...
## $ data.Year_built : num 2005 1994 2013 1900 1968 ...
## - attr(*, "na.action")= 'omit' Named int [1:666] 29 72 90 91 117 169 173 174 181 182 ...
## ..- attr(*, "names")= chr [1:666] "29" "72" "90" "91" ...glm.sq.price <- glm(cbind(data.Price, data.Living_space)~ data.Year_built,
family = "binomial",
data = df.glm)## Warning in eval(family$initialize): non-integer counts in a binomial glm!summary(glm.sq.price)##
## Call:
## glm(formula = cbind(data.Price, data.Living_space) ~ data.Year_built,
## family = "binomial", data = df.glm)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -74.091 -7.312 -1.783 3.161 97.560
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.500558303 0.017151213 204.1 <0.0000000000000002 ***
## data.Year_built 0.002238126 0.000008763 255.4 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 947369 on 9651 degrees of freedom
## Residual deviance: 895142 on 9650 degrees of freedom
## AIC: 963053
##
## Number of Fisher Scoring iterations: 6exp(coef(glm.sq.price))## (Intercept) data.Year_built
## 33.133946 1.002241ggplot(data = df.glm,
mapping = aes(y = data.Price/data.Living_space,
x = data.Year_built)) +
geom_point() +
geom_smooth(method = "glm",
se = FALSE,
method.args = list(family = "binomial"))## `geom_smooth()` using formula 'y ~ x'## Warning: Computation failed in `stat_smooth()`:
## y values must be 0 <= y <= 1
GLM with binomial data factor variable
glm.sq.price <- glm(cbind(Price, Living_space)~ State,
family = "binomial",
data = data)## Warning in eval(family$initialize): non-integer counts in a binomial glm!summary(glm.sq.price)##
## Call:
## glm(formula = cbind(Price, Living_space) ~ State, family = "binomial",
## data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -59.255 -6.366 -1.195 3.473 61.109
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 8.34931 0.09536 87.558 < 0.0000000000000002
## StateBaden-Württemberg -0.26983 0.09538 -2.829 0.004667
## StateBayern -0.11439 0.09538 -1.199 0.230381
## StateBerlin 0.22109 0.09549 2.315 0.020597
## StateBrandenburg -0.34169 0.09542 -3.581 0.000342
## StateBremen -0.45021 0.09601 -4.689 0.000002744267682839
## StateHamburg 0.20992 0.09607 2.185 0.028878
## StateHessen -0.35562 0.09538 -3.728 0.000193
## StateMecklenburg-Vorpommern -0.77292 0.09544 -8.099 0.000000000000000555
## StateNiedersachsen -0.78534 0.09538 -8.234 < 0.0000000000000002
## StateNordrhein-Westfalen -0.52038 0.09537 -5.456 0.000000048613961013
## StateRheinland-Pfalz -0.77836 0.09538 -8.160 0.000000000000000334
## StateSaarland -1.13274 0.09552 -11.859 < 0.0000000000000002
## StateSachsen -1.08280 0.09541 -11.349 < 0.0000000000000002
## StateSachsen-Anhalt -1.36482 0.09544 -14.300 < 0.0000000000000002
## StateSchleswig-Holstein -0.36652 0.09541 -3.842 0.000122
## StateThüringen -1.20943 0.09555 -12.657 < 0.0000000000000002
##
## (Intercept) ***
## StateBaden-Württemberg **
## StateBayern
## StateBerlin *
## StateBrandenburg ***
## StateBremen ***
## StateHamburg *
## StateHessen ***
## StateMecklenburg-Vorpommern ***
## StateNiedersachsen ***
## StateNordrhein-Westfalen ***
## StateRheinland-Pfalz ***
## StateSaarland ***
## StateSachsen ***
## StateSachsen-Anhalt ***
## StateSchleswig-Holstein ***
## StateThüringen ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1039137 on 10317 degrees of freedom
## Residual deviance: 812246 on 10301 degrees of freedom
## AIC: 884878
##
## Number of Fisher Scoring iterations: 5exp(coef(glm.sq.price))## (Intercept) StateBaden-Württemberg
## 4227.2727273 0.7635056
## StateBayern StateBerlin
## 0.8919084 1.2474312
## StateBrandenburg StateBremen
## 0.7105675 0.6374919
## StateHamburg StateHessen
## 1.2335789 0.7007400
## StateMecklenburg-Vorpommern StateNiedersachsen
## 0.4616627 0.4559654
## StateNordrhein-Westfalen StateRheinland-Pfalz
## 0.5942937 0.4591593
## StateSaarland StateSachsen
## 0.3221483 0.3386464
## StateSachsen-Anhalt StateSchleswig-Holstein
## 0.2554273 0.6931439
## StateThüringen
## 0.2983668ggplot(data = data,
mapping = aes(y = Price/Living_space,
x = State)) +
geom_point() +
geom_smooth(method = "glm",
se = FALSE,
method.args = list(family = "binomial"))## `geom_smooth()` using formula 'y ~ x'
If we compare the Residual deviance and the corresponding degrees of freedom in the summary output we would expect in an truly Poisson distributed data hat the residual deviance and the degrees of freedom would be approximately the same value. Therefore it could be overdispersed here and we use the “quasibinomial” family.
glm.sq.price <- glm(cbind(Price, Living_space)~ State,
family = "quasibinomial",
data = data)
summary(glm.sq.price)##
## Call:
## glm(formula = cbind(Price, Living_space) ~ State, family = "quasibinomial",
## data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -59.255 -6.366 -1.195 3.473 61.109
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.3493 0.9998 8.351 <0.0000000000000002 ***
## StateBaden-Württemberg -0.2698 1.0000 -0.270 0.787
## StateBayern -0.1144 1.0000 -0.114 0.909
## StateBerlin 0.2211 1.0012 0.221 0.825
## StateBrandenburg -0.3417 1.0004 -0.342 0.733
## StateBremen -0.4502 1.0066 -0.447 0.655
## StateHamburg 0.2099 1.0072 0.208 0.835
## StateHessen -0.3556 1.0000 -0.356 0.722
## StateMecklenburg-Vorpommern -0.7729 1.0006 -0.772 0.440
## StateNiedersachsen -0.7853 1.0000 -0.785 0.432
## StateNordrhein-Westfalen -0.5204 0.9999 -0.520 0.603
## StateRheinland-Pfalz -0.7784 1.0000 -0.778 0.436
## StateSaarland -1.1327 1.0015 -1.131 0.258
## StateSachsen -1.0828 1.0003 -1.083 0.279
## StateSachsen-Anhalt -1.3648 1.0006 -1.364 0.173
## StateSchleswig-Holstein -0.3665 1.0003 -0.366 0.714
## StateThüringen -1.2094 1.0018 -1.207 0.227
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasibinomial family taken to be 109.9222)
##
## Null deviance: 1039137 on 10317 degrees of freedom
## Residual deviance: 812246 on 10301 degrees of freedom
## AIC: NA
##
## Number of Fisher Scoring iterations: 5exp(coef(glm.sq.price))## (Intercept) StateBaden-Württemberg
## 4227.2727273 0.7635056
## StateBayern StateBerlin
## 0.8919084 1.2474312
## StateBrandenburg StateBremen
## 0.7105675 0.6374919
## StateHamburg StateHessen
## 1.2335789 0.7007400
## StateMecklenburg-Vorpommern StateNiedersachsen
## 0.4616627 0.4559654
## StateNordrhein-Westfalen StateRheinland-Pfalz
## 0.5942937 0.4591593
## StateSaarland StateSachsen
## 0.3221483 0.3386464
## StateSachsen-Anhalt StateSchleswig-Holstein
## 0.2554273 0.6931439
## StateThüringen
## 0.2983668The dispersion parameter ist now 109.92, This implies the variance increases faster than linearly. Anyway in this case there is no evidence that the State have an impact on the response variable.
#install.packages('mltools')
library(mltools)
# Resulting bins have an equal number of observations in each group
data[, "wt2"] <- bin_data(data$Price, bins=4, binType = "quantile")
# Resulting bins are equally spaced from min to max
data[, "wt3"] <- bin_data(data$Price, bins=4, binType = "explicit")
# Or if you'd rather define the bins yourself
data[, "wt4"] <- bin_data(data$Price, bins=c(-Inf, 250, 322, Inf), binType = "explicit")
head(data)## Price Type Living_space Lot Rooms Bedrooms Bathrooms Floors
## 1 498000 Multiple dwelling 106.00 229 5 3 1 2
## 2 495000 Mid-terrace house 140.93 517 6 3 2 NA
## 3 749000 Farmhouse 162.89 82 5 3 2 4
## 4 259000 Farmhouse 140.00 814 4 NA 2 2
## 5 469000 Multiple dwelling 115.00 244 4 2 1 NA
## 6 1400000 Mid-terrace house 310.00 860 8 NA NA 3
## Year_built Furnishing_quality Year_renovated Condition Heating
## 1 2005 normal NA refurbished central heating
## 2 1994 basic NA refurbished stove heating
## 3 2013 NA dilapidated stove heating
## 4 1900 basic 2000 fixer-upper central heating
## 5 1968 refined 2019 refurbished central heating
## 6 1969 basic NA maintained
## Energy_source Energy_efficiency_class State City
## 1 natural gas D Baden-Württemberg Bodenseekreis
## 2 Baden-Württemberg Konstanz (Kreis)
## 3 district heating B Baden-Württemberg Esslingen (Kreis)
## 4 electricity G Baden-Württemberg Waldshut (Kreis)
## 5 oil F Baden-Württemberg Esslingen (Kreis)
## 6 oil Baden-Württemberg Stuttgart
## Place Garages Garagetype wt2
## 1 Bermatingen 2 Parking lot [399000, 649900)
## 2 Engen 7 Parking lot [399000, 649900)
## 3 Ostfildern 1 Garage [649900, 13000000]
## 4 Bonndorf im Schwarzwald 1 Garage [250000, 399000)
## 5 Leinfelden-Echterdingen 1 Garage [399000, 649900)
## 6 Süd 2 Garage [649900, 13000000]
## wt3 wt4
## 1 [10000, 3257500) [322, Inf]
## 2 [10000, 3257500) [322, Inf]
## 3 [10000, 3257500) [322, Inf]
## 4 [10000, 3257500) [322, Inf]
## 5 [10000, 3257500) [322, Inf]
## 6 [10000, 3257500) [322, Inf]glm.roomswt2 <- glm(Rooms ~ wt2,
family = "poisson",
data = data)
summary(glm.roomswt2)##
## Call:
## glm(formula = Rooms ~ wt2, family = "poisson", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.2229 -0.8439 -0.3171 0.4433 4.5174
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.922092 0.003783 508.099 < 0.0000000000000002 ***
## wt2.L 0.235488 0.007507 31.369 < 0.0000000000000002 ***
## wt2.Q 0.056346 0.007566 7.447 0.0000000000000952 ***
## wt2.C 0.041856 0.007624 5.490 0.0000000401941232 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 13951 on 10317 degrees of freedom
## Residual deviance: 12833 on 10314 degrees of freedom
## AIC: 51023
##
## Number of Fisher Scoring iterations: 4set.seed(99)
sim.data.rooms.Poissonwt2 <- simulate(glm.roomswt2)
##
NROW(sim.data.rooms.Poissonwt2)## [1] 10318head(sim.data.rooms.Poissonwt2)## sim_1
## 1 7
## 2 4
## 3 10
## 4 13
## 5 7
## 6 14tail(sim.data.rooms.Poissonwt2)## sim_1
## 10313 10
## 10314 16
## 10315 11
## 10316 5
## 10317 5
## 10318 9library(ggplot2)
ggplot(mapping = aes(y = sim.data.rooms.Poissonwt2$sim_1,
x = data$wt2)) +
geom_boxplot() +
geom_hline(yintercept = 0) +
ylab("simulated no. of rooms\n(assuming Poisson dist)") +
xlab("Groups")
GLM - Binary Model
Let’s fit a binary model
data$MillionYes <- ifelse(data$Price > 1000000, 1, 0)
data$MillionYesLet’s fit a logistic regression model and add fit to the this graph
glm.binary <- glm(MillionYes ~ Living_space,
family = "binomial",
data = data)
ggplot(data = glm.binary,
mapping = aes(y = MillionYes,
x = Living_space)) +
geom_point() +
geom_smooth(method = "glm",
se = FALSE,
method.args = list(family = "binomial")) ## `geom_smooth()` using formula 'y ~ x'
4 Week 4 - Support Vector Machines
data$wt5 <- factor(ifelse(data$Price > 600000, 1, -1))
data$wt5 = as.factor(data$wt5)
str(data)## 'data.frame': 10318 obs. of 25 variables:
## $ Price : num 498000 495000 749000 259000 469000 1400000 3500000 630000 364000 1750000 ...
## $ Type : chr "Multiple dwelling" "Mid-terrace house" "Farmhouse" "Farmhouse" ...
## $ Living_space : num 106 141 163 140 115 ...
## $ Lot : num 229 517 82 814 244 860 5300 406 973 1460 ...
## $ Rooms : int 5 6 5 4 4 8 13 10 10 6 ...
## $ Bedrooms : num 3 3 3 NA 2 NA NA NA 4 4 ...
## $ Bathrooms : num 1 2 2 2 1 NA 4 NA 4 2 ...
## $ Floors : num 2 NA 4 2 NA 3 NA 3 2 3 ...
## $ Year_built : num 2005 1994 2013 1900 1968 ...
## $ Furnishing_quality : chr "normal" "basic" "" "basic" ...
## $ Year_renovated : num NA NA NA 2000 2019 ...
## $ Condition : chr "refurbished" "refurbished" "dilapidated" "fixer-upper" ...
## $ Heating : chr "central heating" "stove heating" "stove heating" "central heating" ...
## $ Energy_source : chr "natural gas" "" "district heating" "electricity" ...
## $ Energy_efficiency_class: chr "D" "" "B" "G" ...
## $ State : chr "Baden-Württemberg" "Baden-Württemberg" "Baden-Württemberg" "Baden-Württemberg" ...
## $ City : chr "Bodenseekreis" "Konstanz (Kreis)" "Esslingen (Kreis)" "Waldshut (Kreis)" ...
## $ Place : chr "Bermatingen" "Engen" "Ostfildern" "Bonndorf im Schwarzwald" ...
## $ Garages : num 2 7 1 1 1 2 7 2 8 2 ...
## $ Garagetype : chr "Parking lot" "Parking lot" "Garage" "Garage" ...
## $ wt2 : Ord.factor w/ 4 levels "[10000, 250000)"<..: 3 3 4 2 3 4 4 3 2 4 ...
## $ wt3 : Ord.factor w/ 4 levels "[10000, 3257500)"<..: 1 1 1 1 1 1 2 1 1 1 ...
## $ wt4 : Ord.factor w/ 3 levels "[-Inf, 250)"<..: 3 3 3 3 3 3 3 3 3 3 ...
## $ MillionYes : num 0 0 0 0 0 1 1 0 0 1 ...
## $ wt5 : Factor w/ 2 levels "-1","1": 1 1 2 1 1 2 2 2 1 2 ...# Load ggplot2
library(ggplot2)
# Plot x2 vs. x1, colored by y
scatter_plot<- ggplot(data = data, aes(x = Living_space, y = Year_built, color = wt2
)) +
# Add a point layer
geom_point() +
scale_color_manual(values = c("red", "blue","green", "purple")) +
# Specify equal coordinates
coord_equal()
scatter_plot ## Warning: Removed 666 rows containing missing values (geom_point).
x1 <- scales::rescale(data$Living_space, to=c(0,1))
x2 <- scales::rescale(data$Year_built, to=c(0,1))
x3 <- scales::rescale(data$Rooms, to=c(0,1))
x4 <- scales::rescale(data$Lot, to=c(0,1))# Load ggplot2
library(ggplot2)
# Plot x2 vs. x1, colored by y
scatter_plot<- ggplot(data = data, aes(x = x1, y = x2, color = wt2
)) +
# Add a point layer
geom_point() +
scale_color_manual(values = c("red", "blue","green", "purple")) +
# Specify equal coordinates
coord_equal()
scatter_plot ## Warning: Removed 666 rows containing missing values (geom_point).
# Load ggplot2
library(ggplot2)
# Plot x2 vs. x1, colored by y
scatter_plot<- ggplot(data = data, aes(x = x1, y = x2, color = wt5
)) +
# Add a point layer
geom_point() +
scale_color_manual(values = c("red", "blue")) +
# Specify equal coordinates
coord_equal()
scatter_plot ## Warning: Removed 666 rows containing missing values (geom_point).
# Load ggplot2
library(ggplot2)
# Plot x2 vs. x1, colored by y
scatter_plot<- ggplot(data = data, aes(x = x1, y = x3, color = wt5
)) +
# Add a point layer
geom_point() +
scale_color_manual(values = c("red", "blue")) +
# Specify equal coordinates
coord_equal()
scatter_plot 
# Load ggplot2
library(ggplot2)
# Plot x2 vs. x1, colored by y
scatter_plot<- ggplot(data = data, aes(x = x1, y = x4, color = wt5
)) +
# Add a point layer
geom_point() +
scale_color_manual(values = c("red", "blue")) +
# Specify equal coordinates
coord_equal()
scatter_plot 
testdf <- data.frame(x2,x1,data$wt5)
print(testdf)## x2 x1 data.wt5
## 1 0.97645429 0.039269950 -1
## 2 0.96121884 0.054565438 -1
## 3 0.98753463 0.064181497 1
## 4 0.83102493 0.054158201 -1
## 5 0.92520776 0.043210958 -1
## 6 0.92659280 0.128599454 1
## 7 0.97506925 0.212674280 1
## 8 0.95429363 0.108018637 1
## 9 0.70498615 0.092254607 -1
## 10 0.88504155 0.084810481 1
## 11 0.93628809 0.110208085 -1
## 12 0.95429363 0.047151965 -1
## 13 0.99307479 0.087875709 1
## 14 0.93905817 0.129002312 1
## 15 0.85041551 0.093568276 1
## 16 0.95983380 0.136481469 1
## 17 0.55124654 0.028414664 -1
## 18 0.94875346 0.079857949 1
## 19 0.95152355 0.050655083 -1
## 20 0.97229917 0.152245498 1
## 21 0.99168975 0.059461045 -1
## 22 0.99307479 0.058467036 1
## 23 0.96121884 0.108894416 1
## 24 0.94321330 0.102326070 1
## 25 0.92659280 0.043210958 -1
## 26 0.99584488 0.060726547 -1
## 27 0.99445983 0.143049814 1
## 28 0.90166205 0.102763960 1
## 29 NA 0.032627163 -1
## 30 0.92243767 0.041021509 -1
## 31 0.90858726 0.076052687 -1
## 32 0.99584488 0.045400406 -1
## 33 0.87811634 0.051092973 -1
## 34 0.95844875 0.178956772 1
## 35 0.90720222 0.090065158 1
## 36 0.95706371 0.042335178 -1
## 37 0.92382271 0.065105444 1
## 38 0.93351801 0.081307364 -1
## 39 0.91966759 0.037080502 -1
## 40 0.92520776 0.099260842 -1
## 41 0.90581717 0.098822952 -1
## 42 0.99584488 0.187714566 1
## 43 0.93905817 0.090809571 -1
## 44 0.90027701 0.041897289 -1
## 45 0.86703601 0.065692216 -1
## 46 0.97368421 0.115462762 1
## 47 0.90443213 0.124220556 1
## 48 0.92243767 0.041021509 -1
## 49 0.91966759 0.043210958 -1
## 50 0.89889197 0.083934702 1
## 51 0.95983380 0.097947173 1
## 52 0.98753463 0.065105444 1
## 53 0.95983380 0.057661319 1
## 54 0.97368421 0.067246725 -1
## 55 0.92105263 0.076052687 1
## 56 0.93905817 0.106704967 1
## 57 0.90581717 0.069046451 1
## 58 0.93351801 0.098315000 -1
## 59 0.94182825 0.065070413 -1
## 60 0.99030471 0.078242136 1
## 61 0.96675900 0.069484341 -1
## 62 0.92520776 0.124220556 -1
## 63 0.93628809 0.092692496 1
## 64 0.65096953 0.084810481 1
## 65 0.93490305 0.048154733 1
## 66 0.93628809 0.104077629 -1
## 67 0.93490305 0.106704967 -1
## 68 0.93213296 0.150931829 -1
## 69 0.97368421 0.053203601 1
## 70 0.95013850 0.080431584 1
## 71 0.99584488 0.065289358 1
## 72 NA 0.146115042 1
## 73 0.92520776 0.495988930 1
## 74 0.95706371 0.182459889 1
## 75 0.90581717 0.041021509 -1
## 76 0.83102493 0.036642612 -1
## 77 0.96260388 0.082621033 1
## 78 0.92797784 0.045400406 -1
## 79 0.93628809 0.062915995 1
## 80 0.94182825 0.146552932 1
## 81 0.96537396 0.114928536 -1
## 82 0.93074792 0.075575387 1
## 83 0.87257618 0.084854270 -1
## 84 0.95290859 0.058974988 1
## 85 0.93767313 0.041021509 -1
## 86 0.87811634 0.102326070 1
## 87 0.87257618 0.064229664 -1
## 88 0.90997230 0.122429587 -1
## 89 0.81440443 0.189904015 1
## 90 NA 0.082183143 1
## 91 NA 0.073425349 -1
## 92 0.92659280 0.060288657 1
## 93 0.91966759 0.049779304 -1
## 94 0.83656510 0.266096826 1
## 95 0.96260388 0.052406642 -1
## 96 0.98060942 0.189904015 1
## 97 0.97229917 0.041021509 -1
## 98 0.92382271 0.118904575 1
## 99 0.96952909 0.084109858 1
## 100 0.96537396 0.111083865 1
## 101 0.96537396 0.077804246 1
## 102 0.98199446 0.048027745 -1
## 103 0.93351801 0.100009634 -1
## 104 0.93490305 0.110208085 1
## 105 0.97091413 0.207419603 1
## 106 0.95152355 0.051968752 1
## 107 0.92520776 0.078719435 1
## 108 0.81855956 0.207419603 1
## 109 0.96814404 0.060398129 -1
## 110 0.93213296 0.109332306 1
## 111 0.94875346 0.073863238 1
## 112 0.94182825 0.082419603 1
## 113 0.94044321 0.041021509 -1
## 114 0.93905817 0.154872837 1
## 115 0.91689751 0.079498879 -1
## 116 0.91966759 0.054158201 -1
## 117 NA 0.049779304 -1
## 118 0.91274238 0.060726547 -1
## 119 0.97229917 0.037956281 1
## 120 0.93767313 0.070360121 -1
## 121 0.92797784 0.114149093 1
## 122 0.96814404 0.141736145 1
## 123 0.97645429 0.127723674 1
## 124 0.99722992 0.066419113 1
## 125 0.93351801 0.091816717 -1
## 126 0.57063712 0.106704967 -1
## 127 0.96121884 0.066419113 -1
## 128 0.83102493 0.133854130 1
## 129 0.86842105 0.065105444 1
## 130 0.96537396 0.069922231 -1
## 131 0.96814404 0.091094199 1
## 132 0.90720222 0.081745253 1
## 133 0.92243767 0.156042002 1
## 134 0.91966759 0.062145309 -1
## 135 0.93628809 0.111083865 -1
## 136 0.82548476 0.073425349 -1
## 137 0.97506925 0.069484341 1
## 138 0.89889197 0.027884817 -1
## 139 0.89889197 0.069484341 1
## 140 0.92382271 0.099260842 1
## 141 0.85872576 0.092254607 -1
## 142 0.80193906 0.054158201 -1
## 143 0.93628809 0.105391298 1
## 144 0.94182825 0.047589855 -1
## 145 0.90858726 0.047151965 -1
## 146 0.92520776 0.220556295 1
## 147 0.91689751 0.091378827 -1
## 148 0.93351801 0.049341414 -1
## 149 0.95013850 0.065105444 -1
## 150 0.91966759 0.083058922 -1
## 151 0.95013850 0.156304736 1
## 152 0.97783934 0.051530862 -1
## 153 0.95290859 0.064667554 1
## 154 0.84626039 0.169323198 1
## 155 0.96260388 0.069922231 1
## 156 0.81855956 0.045400406 -1
## 157 0.91412742 0.071673790 1
## 158 0.92797784 0.153997057 1
## 159 0.99307479 0.081307364 -1
## 160 0.91966759 0.028957647 1
## 161 0.94182825 0.084810481 -1
## 162 0.97368421 0.058099208 1
## 163 0.96121884 0.027324319 -1
## 164 0.95152355 0.094444055 1
## 165 0.94321330 0.065981223 -1
## 166 0.88088643 0.164506411 1
## 167 0.91412742 0.079993694 -1
## 168 0.99307479 0.039261192 -1
## 169 NA 0.062915995 -1
## 170 0.96952909 0.131765396 1
## 171 0.96398892 0.286239753 1
## 172 0.83102493 0.069484341 -1
## 173 NA 0.100574511 1
## 174 NA 0.097071394 -1
## 175 0.90443213 0.036642612 -1
## 176 0.83102493 0.024819589 -1
## 177 0.89335180 0.045400406 -1
## 178 0.93213296 0.060288657 -1
## 179 0.93490305 0.085686261 -1
## 180 0.95844875 0.146115042 1
## 181 NA 0.080431584 1
## 182 NA 0.049779304 -1
## 183 NA 0.038394171 -1
## 184 0.93213296 0.076052687 1
## 185 0.93213296 0.127723674 1
## 186 0.90443213 0.159326175 1
## 187 0.76177285 0.054727457 -1
## 188 0.84487535 0.128857808 1
## 189 0.90166205 0.089189379 1
## 190 0.73130194 0.113711203 -1
## 191 NA 0.034453163 -1
## 192 0.91551247 0.051968752 -1
## 193 0.91412742 0.036642612 -1
## 194 0.95013850 0.106704967 1
## 195 0.91274238 0.076052687 1
## 196 0.91274238 0.076052687 1
## 197 0.83102493 0.150493940 -1
## 198 0.94598338 0.077804246 -1
## 199 0.97506925 0.073863238 -1
## 200 0.84487535 0.081745253 1
## 201 0.92243767 0.128599454 1
## 202 0.97091413 0.047589855 1
## 203 0.94044321 0.037080502 -1
## 204 0.97783934 0.078242136 1
## 205 0.93905817 0.069484341 -1
## 206 0.92382271 0.095319835 1
## 207 NA 0.090065158 1
## 208 0.98753463 0.089627268 1
## 209 0.93905817 0.146115042 1
## 210 0.93628809 0.106704967 1
## 211 NA 0.069046451 1
## 212 0.83795014 0.049779304 -1
## 213 0.86288089 0.057661319 1
## 214 0.91412742 0.216851748 1
## 215 0.92243767 0.056785539 -1
## 216 0.90858726 0.046276186 -1
## 217 0.98753463 0.062915995 -1
## 218 0.90443213 0.130788902 1
## 219 0.93490305 0.038394171 -1
## 220 0.93905817 0.117214321 1
## 221 0.83518006 0.044962517 -1
## 222 0.95706371 0.134165032 1
## 223 0.99168975 0.051968752 -1
## 224 0.80193906 0.121155328 1
## 225 0.82825485 0.107580747 1
## 226 0.98337950 0.132978351 1
## 227 0.95567867 0.115261333 1
## 228 0.83102493 0.052406642 -1
## 229 0.37257618 0.135167799 1
## 230 0.37257618 0.135167799 1
## 231 0.94044321 0.288665662 1
## 232 0.94459834 0.084810481 -1
## 233 0.90581717 0.033139494 -1
## 234 0.91551247 0.096099278 1
## 235 0.98614958 0.120279549 1
## 236 0.99445983 0.106704967 1
## 237 0.94321330 0.122031108 1
## 238 0.91966759 0.144363484 1
## 239 0.91412742 0.069046451 1
## 240 0.94182825 0.057223429 -1
## 241 0.97229917 0.097947173 1
## 242 0.91274238 0.106704967 1
## 243 0.93767313 0.076928466 1
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## 1654 0.95706371 0.072926154 -1
## 1655 0.97645429 0.058537098 -1
## 1656 0.99168975 0.065105444 1
## 1657 0.97506925 0.061952638 1
## 1658 0.96121884 0.095757724 1
## 1659 0.98337950 0.045400406 -1
## 1660 0.92243767 0.069484341 -1
## 1661 0.94044321 0.081307364 -1
## 1662 0.99307479 0.047589855 -1
## 1663 0.98753463 0.047589855 1
## 1664 0.94182825 0.115900652 -1
## 1665 0.97645429 0.056785539 -1
## 1666 0.95429363 0.115462762 1
## 1667 0.97368421 0.063791775 1
## 1668 0.92936288 0.109332306 1
## 1669 0.93351801 0.061602326 1
## 1670 0.90027701 0.047589855 -1
## 1671 0.96537396 0.030074266 -1
## 1672 0.93351801 0.075128740 -1
## 1673 0.87811634 0.102326070 1
## 1674 0.99030471 0.076052687 -1
## 1675 0.97368421 0.049779304 -1
## 1676 0.99584488 0.356302109 1
## 1677 0.95429363 0.085248371 1
## 1678 0.94321330 0.056347649 1
## 1679 0.94459834 0.111083865 1
## 1680 0.95844875 0.080431584 -1
## 1681 0.93074792 0.074301128 1
## 1682 0.96814404 0.036879072 -1
## 1683 0.93767313 0.056347649 -1
## 1684 0.95013850 0.071673790 1
## 1685 0.99584488 0.098822952 1
## 1686 0.91966759 0.067294892 1
## 1687 0.93490305 0.058537098 -1
## 1688 0.93628809 0.084810481 -1
## 1689 0.96260388 0.115462762 -1
## 1690 0.99445983 0.064264696 1
## 1691 0.95706371 0.156186506 -1
## 1692 0.77562327 0.222745744 1
## 1693 0.95429363 0.108018637 1
## 1694 NA 0.044086737 1
## 1695 NA 0.075614797 1
## 1696 0.96537396 0.059710642 -1
## 1697 0.96537396 0.059710642 -1
## 1698 0.94182825 0.079555805 1
## 1699 0.93905817 0.078242136 -1
## 1700 0.93628809 0.063353885 -1
## 1701 0.99445983 0.054815035 1
## 1702 0.94044321 0.063353885 1
## 1703 0.99722992 0.101888180 -1
## 1704 0.87811634 0.039177993 1
## 1705 0.87257618 0.173264205 1
## 1706 0.98753463 0.098428852 1
## 1707 0.98753463 0.053764100 -1
## 1708 0.98753463 0.037518391 -1
## 1709 NA 0.153602957 -1
## 1710 0.81717452 0.121155328 -1
## 1711 0.97091413 0.132540461 1
## 1712 0.95844875 0.089189379 1
## 1713 0.91135734 0.073863238 -1
## 1714 0.62326870 0.146115042 -1
## 1715 NA 0.108456526 1
## 1716 0.90997230 0.031387935 1
## 1717 0.98891967 0.069484341 1
## 1718 0.95983380 0.074739018 1
## 1719 0.95429363 0.080869474 1
## 1720 0.99722992 0.046477615 -1
## 1721 0.91689751 0.036642612 -1
## 1722 0.95844875 0.065981223 1
## 1723 0.93074792 0.077366356 1
## 1724 0.82409972 0.137357248 1
## 1725 0.62326870 0.260404260 1
## 1726 0.96121884 0.102326070 1
## 1727 0.83379501 0.086562040 1
## 1728 NA 0.051530862 -1
## 1729 0.93213296 0.080431584 1
## 1730 0.94459834 0.101012401 -1
## 1731 0.93628809 0.059412877 -1
## 1732 NA 0.096633504 1
## 1733 0.99168975 0.060726547 -1
## 1734 0.97922438 0.071235900 1
## 1735 0.95844875 0.034453163 -1
## 1736 0.92382271 0.119841659 -1
## 1737 0.91412742 0.045400406 -1
## 1738 0.94459834 0.058537098 -1
## 1739 0.93628809 0.068170672 1
## 1740 0.81578947 0.218366846 -1
## 1741 NA 0.032263715 -1
## 1742 0.96260388 0.106704967 1
## 1743 0.94875346 0.036204722 -1
## 1744 0.98476454 0.100035907 1
## 1745 0.96952909 0.089189379 1
## 1746 0.88642659 0.157062285 1
## 1747 0.98753463 0.029636376 -1
## 1748 0.92243767 0.130351012 1
## 1749 0.98753463 0.089189379 1
## 1750 0.83102493 0.058537098 -1
## 1751 0.83102493 0.058537098 -1
## 1752 0.96952909 0.072549569 -1
## 1753 0.97368421 0.101450291 1
## 1754 0.94182825 0.108456526 -1
## 1755 0.99168975 0.056785539 -1
## 1756 0.97368421 0.057424858 -1
## 1757 NA 0.080431584 -1
## 1758 0.95567867 0.053720311 1
## 1759 0.96675900 0.069681391 1
## 1760 0.96121884 0.062158446 -1
## 1761 0.91412742 0.058537098 -1
## 1762 0.93213296 0.106862608 1
## 1763 0.91966759 0.054158201 -1
## 1764 0.95429363 0.056347649 1
## 1765 0.92797784 0.047589855 -1
## 1766 0.94736842 0.124220556 -1
## 1767 0.89058172 0.260842150 1
## 1768 0.83656510 0.227562531 1
## 1769 0.88227147 0.112397534 -1
## 1770 0.93628809 0.089189379 -1
## 1771 0.91412742 0.102763960 -1
## 1772 0.91412742 0.183773558 1
## 1773 0.97783934 0.124220556 1
## 1774 0.90027701 0.095319835 1
## 1775 0.98891967 0.076928466 -1
## 1776 0.38781163 0.209609052 1
## 1777 0.95152355 0.086999930 1
## 1778 0.87119114 0.050217193 -1
## 1779 0.92382271 0.037518391 1
## 1780 0.94459834 0.277919849 -1
## 1781 0.92797784 0.084810481 -1
## 1782 0.99584488 0.053282421 -1
## 1783 0.97506925 0.045400406 1
## 1784 0.91551247 0.121155328 1
## 1785 0.96675900 0.140860366 1
## 1786 0.96121884 0.062915995 -1
## 1787 0.99722992 0.075430883 1
## 1788 0.92936288 0.085686261 1
## 1789 0.93351801 0.108894416 1
## 1790 0.97645429 0.083934702 1
## 1791 0.94736842 0.053063476 1
## 1792 0.92243767 0.103201850 1
## 1793 0.96675900 0.038832061 -1
## 1794 0.92797784 0.255587473 -1
## 1795 0.91274238 0.041021509 -1
## 1796 0.94321330 0.054158201 -1
## 1797 0.94321330 0.064229664 1
## 1798 0.98753463 0.325649828 1
## 1799 0.95013850 0.075614797 -1
## 1800 0.92520776 0.144363484 1
## 1801 0.94182825 0.099260842 1
## 1802 0.99307479 0.093831010 1
## 1803 0.99445983 0.061164436 -1
## 1804 0.92243767 0.040548588 1
## 1805 0.92797784 0.071673790 -1
## 1806 0.96952909 0.069922231 1
## 1807 0.94182825 0.117652210 1
## 1808 0.97922438 0.099532334 -1
## 1809 0.86980609 0.078242136 1
## 1810 0.95983380 0.045400406 -1
## 1811 0.91412742 0.049779304 -1
## 1812 NA 0.045400406 -1
## 1813 0.94321330 0.071673790 -1
## 1814 0.88088643 0.054158201 -1
## 1815 0.91412742 0.057661319 1
## 1816 0.91412742 0.041021509 -1
## 1817 0.98476454 0.080431584 1
## 1818 0.99445983 0.048027745 1
## 1819 0.95567867 0.058099208 1
## 1820 0.92936288 0.043648847 -1
## 1821 0.97645429 0.080431584 1
## 1822 0.97229917 0.051968752 -1
## 1823 0.96537396 0.077116759 1
## 1824 0.92659280 0.080431584 -1
## 1825 NA 0.054158201 -1
## 1826 NA 0.130543684 1
## 1827 0.81717452 0.158813844 -1
## 1828 0.96121884 0.125972115 -1
## 1829 0.95844875 0.102326070 1
## 1830 0.92382271 0.110208085 1
## 1831 0.90997230 0.058974988 -1
## 1832 0.68975069 0.084810481 1
## 1833 0.99307479 0.089189379 1
## 1834 0.84903047 0.058537098 -1
## 1835 0.97091413 0.117652210 1
## 1836 0.95013850 0.124220556 -1
## 1837 0.93628809 0.085686261 -1
## 1838 0.95429363 0.054596091 1
## 1839 0.98337950 0.185525117 1
## 1840 0.78947368 0.309010019 -1
## 1841 0.99584488 0.084372592 -1
## 1842 0.84764543 0.071673790 -1
## 1843 0.70498615 0.184211448 1
## 1844 0.88642659 0.211798501 1
## 1845 0.98060942 0.065582744 1
## 1846 0.99584488 0.045400406 1
## 1847 0.95152355 0.106704967 1
## 1848 0.97506925 0.139108807 1
## 1849 0.93905817 0.102326070 1
## 1850 0.94875346 0.076052687 -1
## 1851 0.99722992 0.079555805 1
## 1852 0.91135734 0.067732782 -1
## 1853 0.91689751 0.040583619 -1
## 1854 0.94459834 0.067294892 1
## 1855 0.99307479 0.060726547 1
## 1856 0.91828255 0.024381700 -1
## 1857 0.98614958 0.057661319 1
## 1858 NA 0.060288657 -1
## 1859 NA 0.154872837 -1
## 1860 NA 0.058537098 -1
## 1861 0.93905817 0.089189379 1
## 1862 0.91689751 0.102326070 1
## 1863 NA 0.077366356 -1
## 1864 NA 0.049779304 -1
## 1865 NA 0.062915995 -1
## 1866 0.90720222 0.089189379 -1
## 1867 0.96814404 0.043210958 -1
## 1868 0.93490305 0.049341414 -1
## 1869 0.93490305 0.075176907 -1
## 1870 0.93490305 0.113058747 -1
## 1871 0.96260388 0.121155328 -1
## 1872 0.93074792 0.048465634 -1
## 1873 0.97368421 0.062915995 1
## 1874 0.99445983 0.062915995 1
## 1875 0.91412742 0.048684579 1
## 1876 0.98753463 0.106704967 1
## 1877 0.95983380 0.185525117 1
## 1878 0.99584488 0.049779304 1
## 1879 0.95152355 0.046714076 1
## 1880 0.95429363 0.054158201 1
## 1881 0.80332410 0.133972360 1
## 1882 0.83102493 0.096633504 -1
## 1883 0.97506925 0.107142857 -1
## 1884 0.93628809 0.102326070 -1
## 1885 0.93628809 0.102326070 -1
## 1886 0.94736842 0.070079871 -1
## 1887 0.95429363 0.054596091 -1
## 1888 0.92797784 0.054158201 -1
## 1889 0.97922438 0.042335178 -1
## 1890 0.97645429 0.117652210 -1
## 1891 0.95844875 0.119403769 1
## 1892 0.95567867 0.059412877 -1
## 1893 0.99861496 0.095757724 1
## 1894 0.90027701 0.016499685 -1
## 1895 0.69252078 0.212529777 -1
## 1896 0.88642659 0.071673790 -1
## 1897 0.92105263 0.085248371 -1
## 1898 0.94459834 0.050309150 -1
## 1899 0.84764543 0.132978351 -1
## 1900 0.96260388 0.171512646 1
## 1901 0.93767313 0.056785539 1
## 1902 0.81717452 0.220556295 1
## 1903 0.91828255 0.044853044 -1
## 1904 0.90027701 0.137357248 1
## 1905 0.98337950 0.071673790 1
## 1906 0.91412742 0.045400406 -1
## 1907 0.94875346 0.080431584 1
## 1908 0.92936288 0.118090100 1
## 1909 0.96952909 0.054158201 -1
## 1910 0.99861496 0.050440517 -1
## 1911 0.94182825 0.213112170 1
## 1912 0.97922438 0.071673790 1
## 1913 0.99722992 0.061484096 -1
## 1914 0.94736842 0.089189379 1
## 1915 0.92105263 0.132978351 1
## 1916 0.83102493 0.097947173 -1
## 1917 0.93074792 0.099260842 -1
## 1918 0.96814404 0.058537098 -1
## 1919 0.98060942 0.111083865 1
## 1920 0.96398892 0.055033980 -1
## 1921 0.96398892 0.055033980 -1
## 1922 0.93351801 0.100574511 -1
## 1923 0.95429363 0.056347649 -1
## 1924 NA 0.143925594 1
## 1925 0.91689751 0.094881945 1
## 1926 0.98891967 0.097728228 1
## 1927 0.95013850 0.042554123 1
## 1928 0.94459834 0.065105444 1
## 1929 NA 0.097947173 -1
## 1930 NA 0.142611925 -1
## 1931 0.99722992 0.046714076 -1
## 1932 0.91828255 0.146115042 -1
## 1933 0.99445983 0.080431584 -1
## 1934 0.88227147 0.036642612 -1
## 1935 0.90027701 0.041021509 -1
## 1936 0.98614958 0.058537098 -1
## 1937 0.88642659 0.078242136 -1
## 1938 0.93074792 0.080431584 1
## 1939 0.92105263 0.087437820 -1
## 1940 0.99307479 0.064667554 -1
## 1941 0.83795014 0.152683388 1
## 1942 0.96675900 0.073863238 -1
## 1943 0.97922438 0.097947173 1
## 1944 0.91412742 0.069922231 1
## 1945 0.99307479 0.061164436 1
## 1946 0.97229917 0.058537098 -1
## 1947 0.91274238 0.071673790 -1
## 1948 0.92520776 0.042773068 -1
## 1949 0.83102493 0.053282421 -1
## 1950 0.92659280 0.108018637 -1
## 1951 0.99722992 0.056347649 -1
## 1952 NA 0.051092973 -1
## 1953 0.91966759 0.114149093 -1
## 1954 0.91689751 0.089189379 -1
## 1955 0.89889197 0.102326070 -1
## 1956 0.93074792 0.073425349 -1
## 1957 0.95567867 0.115462762 1
## 1958 0.95983380 0.168009528 1
## 1959 0.69252078 0.101450291 -1
## 1960 0.97783934 0.071235900 1
## 1961 NA 0.056347649 -1
## 1962 0.94321330 0.059412877 1
## 1963 0.95429363 0.067294892 1
## 1964 0.85872576 0.118965880 -1
## 1965 0.91966759 0.039059763 -1
## 1966 0.90997230 0.048027745 -1
## 1967 0.96952909 0.143925594 1
## 1968 0.96952909 0.051968752 -1
## 1969 0.88088643 0.106704967 -1
## 1970 0.97368421 0.074301128 -1
## 1971 0.95429363 0.146115042 1
## 1972 0.94321330 0.054158201 1
## 1973 0.93351801 0.058537098 -1
## 1974 0.97783934 0.082183143 -1
## 1975 0.98891967 0.068608562 1
## 1976 0.91966759 0.060726547 1
## 1977 0.91689751 0.047589855 -1
## 1978 0.98199446 0.060726547 -1
## 1979 NA 0.062915995 1
## 1980 0.98337950 0.045400406 -1
## 1981 0.88088643 0.055909760 -1
## 1982 0.91412742 0.147450606 1
## 1983 0.62326870 0.054158201 -1
## 1984 0.94044321 0.161541897 1
## 1985 0.94736842 0.102326070 1
## 1986 0.96952909 0.086999930 -1
## 1987 0.92936288 0.049779304 -1
## 1988 0.96121884 0.075860015 1
## 1989 0.98476454 0.051530862 1
## 1990 0.91135734 0.067294892 -1
## 1991 0.99168975 0.065543334 1
## 1992 0.99307479 0.081307364 1
## 1993 0.95706371 0.058974988 -1
## 1994 0.99584488 0.046276186 -1
## 1995 0.93074792 0.051968752 1
## 1996 0.99722992 0.069046451 -1
## 1997 0.99030471 0.181146220 1
## 1998 NA 0.055471870 1
## 1999 0.62326870 0.052406642 -1
## 2000 NA 0.045400406 1
## 2001 0.95567867 0.062915995 -1
## 2002 0.91412742 0.036642612 -1
## 2003 0.90581717 0.043210958 -1
## 2004 0.96814404 0.027009038 -1
## 2005 0.87950139 0.067294892 -1
## 2006 0.97783934 0.108145625 1
## 2007 0.92243767 0.046276186 -1
## 2008 0.95706371 0.049779304 -1
## 2009 0.91412742 0.070798010 -1
## 2010 0.94321330 0.094881945 -1
## 2011 0.93905817 0.061164436 -1
## 2012 0.96814404 0.061164436 -1
## 2013 0.83102493 0.106310867 1
## 2014 0.96814404 0.045400406 -1
## 2015 0.92382271 0.037518391 -1
## 2016 0.94321330 0.102326070 -1
## 2017 0.98753463 0.102326070 -1
## 2018 0.94736842 0.107580747 -1
## 2019 0.99168975 0.059158901 -1
## 2020 0.90027701 0.023505920 -1
## 2021 0.90166205 0.076052687 -1
## 2022 0.83240997 0.061637357 -1
## 2023 0.97368421 0.113273313 1
## 2024 0.84903047 0.312513137 1
## 2025 0.90581717 0.056347649 -1
## 2026 0.90027701 0.073863238 -1
## 2027 0.96952909 0.043648847 -1
## 2028 0.99030471 0.053216738 1
## 2029 0.87396122 0.082183143 1
## 2030 0.94598338 0.111083865 1
## 2031 0.96952909 0.052520493 1
## 2032 0.91828255 0.076928466 -1
## 2033 0.93074792 0.059850767 1
## 2034 0.93074792 0.076052687 -1
## 2035 0.98476454 0.053282421 1
## 2036 0.92243767 0.080431584 -1
## 2037 0.99307479 0.049341414 -1
## 2038 NA 0.047589855 1
## 2039 0.91966759 0.045400406 -1
## 2040 0.93074792 0.097947173 1
## 2041 0.92936288 0.062915995 -1
## 2042 0.95013850 0.080431584 1
## 2043 0.85872576 0.073863238 -1
## 2044 0.90443213 0.061786240 -1
## 2045 0.85872576 0.071673790 -1
## 2046 0.93628809 0.049779304 1
## 2047 0.99584488 0.043648847 1
## 2048 0.92659280 0.062915995 -1
## 2049 0.94736842 0.126410005 1
## 2050 0.93074792 0.124220556 1
## 2051 0.87673130 0.097947173 -1
## 2052 0.92520776 0.045400406 -1
## 2053 0.91551247 0.027884817 -1
## 2054 0.95152355 0.055471870 -1
## 2055 0.98753463 0.057223429 -1
## 2056 0.95152355 0.062478106 -1
## 2057 0.93490305 0.130351012 1
## 2058 0.96952909 0.049779304 -1
## 2059 0.91274238 0.036642612 -1
## 2060 0.97368421 0.062915995 -1
## 2061 0.95429363 0.080431584 1
## 2062 0.96121884 0.132102571 1
## 2063 0.93074792 0.056347649 1
## 2064 0.96121884 0.056347649 -1
## 2065 0.98753463 0.041459399 1
## 2066 0.87950139 0.041021509 -1
## 2067 0.93905817 0.062915995 1
## 2068 0.51246537 0.122031108 -1
## 2069 0.97783934 0.041021509 -1
## 2070 0.95429363 0.048448119 -1
## 2071 0.91828255 0.071673790 -1
## 2072 0.97922438 0.102326070 1
## 2073 0.87950139 0.027884817 -1
## 2074 0.86980609 0.102326070 -1
## 2075 0.76177285 0.048640790 -1
## 2076 0.92520776 0.054158201 -1
## 2077 0.93074792 0.103858684 -1
## 2078 0.89889197 0.032263715 -1
## 2079 0.98060942 0.047589855 1
## 2080 0.83795014 0.102326070 -1
## 2081 0.95013850 0.062915995 -1
## 2082 0.94459834 0.051968752 -1
## 2083 0.92382271 0.048903524 1
## 2084 0.88365651 0.048903524 -1
## 2085 0.94182825 0.099260842 1
## 2086 0.96537396 0.058974988 -1
## 2087 0.95983380 0.070360121 -1
## 2088 0.80332410 0.045400406 -1
## 2089 0.97506925 0.056347649 1
## 2090 0.92520776 0.051530862 1
## 2091 0.97783934 0.042773068 -1
## 2092 0.93628809 0.124220556 1
## 2093 0.95429363 0.055909760 -1
## 2094 0.91966759 0.055471870 -1
## 2095 0.34626039 0.124220556 -1
## 2096 0.97645429 0.036642612 1
## 2097 0.91828255 0.059412877 -1
## 2098 0.91966759 0.080431584 1
## 2099 0.99168975 0.125534225 1
## 2100 0.80332410 0.111083865 -1
## 2101 0.94875346 0.072549569 -1
## 2102 0.88504155 0.032263715 -1
## 2103 NA 0.051990647 -1
## 2104 0.92797784 0.125096336 -1
## 2105 0.96121884 0.072549569 1
## 2106 0.95983380 0.075614797 -1
## 2107 0.96537396 0.044086737 1
## 2108 0.90166205 0.061865060 -1
## 2109 0.96537396 0.037080502 -1
## 2110 0.99445983 0.062136552 1
## 2111 0.90720222 0.144801373 1
## 2112 0.84903047 0.119841659 1
## 2113 0.88088643 0.124220556 1
## 2114 0.97645429 0.051092973 -1
## 2115 0.90581717 0.023505920 -1
## 2116 0.94321330 0.049779304 1
## 2117 0.89612188 0.065105444 -1
## 2118 0.94736842 0.187714566 1
## 2119 0.83102493 0.168009528 1
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## 10307 NA 0.146115042 1
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## 10311 0.99584488 0.104077629 1
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## 10316 0.99861496 0.055033980 1
## 10317 0.99584488 0.045763855 -1
## 10318 0.99030471 0.056347649 1#install.packages("e1071")
library(e1071)##
## Attaching package: 'e1071'## The following object is masked from 'package:mltools':
##
## skewness# Print average accuracy and standard deviation
accuracy <- rep(NA, 100)
set.seed(2)
# Calculate accuracies for 100 training/test partitions
for (i in 1:100){
testdf[, "train"] <- ifelse(runif(nrow(testdf)) < 0.8, 1, 0)
trainset <- testdf[testdf$train == 1, ]
testset <- testdf[testdf$train == 0, ]
trainColNum <- grep("train", names(trainset))
trainset <- trainset[, -trainColNum]
testset <- testset[, -trainColNum]
svm_model <- svm(data.wt5 ~ ., data = trainset, type = "C-classification", kernel = "linear")
pred_test <- predict(svm_model, testset)
accuracy[i] <- mean(pred_test == testset$data.wt5)
}
# Print average accuracy and standard deviation
mean(accuracy)## [1] 0.6886003sd(accuracy)## [1] 0.009164209plot(svm_model,testset)
# Print average accuracy and standard deviation
accuracy <- rep(NA, 10)
set.seed(2)
# Calculate accuracies for 100 training/test partitions
for (i in 1:10){
testdf[, "train"] <- ifelse(runif(nrow(testdf)) < 0.8, 1, 0)
trainset <- testdf[testdf$train == 1, ]
testset <- testdf[testdf$train == 0, ]
trainColNum <- grep("train", names(trainset))
trainset <- trainset[, -trainColNum]
testset <- testset[, -trainColNum]
svm_model <- svm(data.wt5 ~ ., data = trainset, type = "C-classification", kernel = "radial")
pred_test <- predict(svm_model, testset)
accuracy[i] <- mean(pred_test == testset$data.wt5)
}
# Print average accuracy and standard deviation
mean(accuracy)## [1] 0.6656181sd(accuracy)## [1] 0.007764355plot(svm_model,testset)
5 Week 5 - Neural Networks
5.1 ANN - neuralnet package
preparing data for neuralnet
library(tidyverse)
library(data.table)##
## Attaching package: 'data.table'## The following objects are masked from 'package:dplyr':
##
## between, first, last## The following object is masked from 'package:purrr':
##
## transposelibrary(neuralnet)##
## Attaching package: 'neuralnet'## The following object is masked from 'package:dplyr':
##
## computelibrary(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## lift## The following object is masked from 'package:survival':
##
## cluster#str(data)
#apply(data,2,function(x) sum(is.na(x)))
df <- data.frame(data$Price, data$Living_space, data$Lot, data$Rooms, data$Year_built, data$Garages)
df.house <- na.omit(df)
#dummy <- dummyVars(" ~ .", data=df.house)
#df.house <- data.frame(predict(dummy, newdata = df.house))
any(is.na(df.house))## [1] FALSEstr(df.house)## 'data.frame': 7974 obs. of 6 variables:
## $ data.Price : num 498000 495000 749000 259000 469000 1400000 3500000 630000 364000 1750000 ...
## $ data.Living_space: num 106 141 163 140 115 ...
## $ data.Lot : num 229 517 82 814 244 860 5300 406 973 1460 ...
## $ data.Rooms : int 5 6 5 4 4 8 13 10 10 6 ...
## $ data.Year_built : num 2005 1994 2013 1900 1968 ...
## $ data.Garages : num 2 7 1 1 1 2 7 2 8 2 ...
## - attr(*, "na.action")= 'omit' Named int [1:2344] 25 26 29 38 44 50 57 70 72 75 ...
## ..- attr(*, "names")= chr [1:2344] "25" "26" "29" "38" ...mean(data$Price)## [1] 540586.6Prepare for Training
Fit the Network
And calculate the RMSE
5.2 ANN - caret package
#str(df.house)
set.seed(42)
tuGrid <- expand.grid(.layer1=c(1:4), .layer2=c(0,2), .layer3=c(0))
trCtrl <- trainControl(
method = 'repeatedcv',
number = 5,
repeats = 5,
returnResamp = 'final'
)
models <- train(
x = df.house %>% select(-data.Price),
y = df.house_scaled %>% pull(data.Price),
method = 'neuralnet', metric = 'RMSE',
linear.output = TRUE,
#be careful, does only work on x!
preProcess = c('center', 'scale'),
tuneGrid = tuGrid,
trControl = trCtrl
)plot(models)plot(models$finalModel)6 Week 6 - Agent-based Modelling and Approximate Bayesian Computation
6.1 Result
ABM